The time evolution of the non-thermal electrons spectrum \(N_e(p,t)\) , written as a function of the time \(t\)  and the normalized momentum \(p=\beta \gamma \) , is given the following equation [1]}:
\(\frac{\partial N_e(p,t)}{\partial t} = \frac{\partial }{\partial p} \left[ \left(-\frac{2}{p}D_{pp}+\sum _i b_i (p) \right) N_e(p,t) + D_{pp}\frac{\partial N_e(p,t)}{\partial p}\right],\) 
